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First principles analysis of graphene and its ability to maintain long-ranged interaction with H2S
Surface Science 621 (2014) 168–174
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First principles analysis of graphene and its ability to maintain long-ranged interaction with H2S Vinay I. Hegde a, Sharmila N. Shirodkar a, Nacir Tit b,⁎, Umesh V. Waghmare a, Zain H. Yamani c a b c
Theoretical Sciences Unit and Sheikh Saqr Laboratory, Jawaharlal Nehru Center for Advanced Scientific Research, Bangalore 560 064, India Physics Department, UAE University, P.O. Box 17551, Al-Ain, United Arab Emirates Center for Research Excellence in Nanotechnology, King Fahd University of Petroleum and Minerals, P.O. Box 5040, 31261 Dhahran, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 3 June 2013 Accepted 23 November 2013 Available online 1 December 2013 Keywords: Electronic structure of graphene Impurity and defect levels Adsorption kinetics Desorption kinetics
a b s t r a c t We determine the chemical activity of (a) carbon site of pristine graphene, (b) Stone–Wales (SW) defect site, and (c) BN-sites of BN-doped graphene towards adsorption of a toxic gas H2S, through comparative analysis based on first-principles density functional theoretical calculations incorporating van der Waals (vdW) interactions. While the adsorption of H2S is weak at both C and BN sites with a binding energy of 15 k J/mol, it is significantly stronger at the Stone–Wales defect site with a much higher binding energy of 26 k J/mol. This is clearly reflected in the contrasting orientation of H2S molecule in the relaxed geometries: the sulfur atom of H2S is closer to graphene (at a distance 3.14 Å) during physisorption at C and BN sites, while the molecule's H atoms come closer to graphene (at a distance 2.84 Å) during physisorption at the Stone–Wales defect site. The origin of the stronger binding interaction between H2S and a SW defect site is attributed to two possible reasons: (i) an increase in the vdW interaction; and (ii) the lowering of both energy of the HOMO level and the total energy of the H2S molecule in attaining a stable configuration. Our findings are compared to the available theoretical results and their technological relevance is further discussed. © 2013 Published by Elsevier B.V.
1. Introduction The pioneering research work of Geim and Novoselov [1] on graphene has opened up a new horizon for fundamental research, and a wide range of advanced technological applications [2]. Graphene possesses unique combination of mechanical strength and flexibility, structural and electronic properties, which makes it attractive for materials engineering. The electronic structure of graphene exhibits linear dispersion near the Fermi level (i.e., Dirac cones at K-points of the Brillouin zone). As a result, effective dynamics of electrons in graphene is that of a massless Dirac (relativistic) fermion, and graphene's electron mobility is rather high (~ 105 cm2 V−1 s−1) [1]. These properties are advantageous in the development of high-speed next generation devices with characteristics exceeding those of silicon and conventional semiconductors. Applications of graphene are quite diverse and relate to interesting physical mechanisms: (1) nanoelectronics (e.g., synthesis of the smallest transistor [3]); (2) photonics (e.g., band-gap engineering using quantum confinement effects in nano-ribbons [4], and BN doping [5]); (3) spintronics (e.g., induction of ferromagnetism by the adsorbed hydrogen atoms in nanoribbons [6]); and (4) gas sensing (e.g., ability to detect several gases like CO, CO2, NO, NO2 and NH3 [7,8]). A very nice coverage of physical challenges involved in making graphene as the ⁎ Corresponding author. E-mail address: [email protected] (N. Tit). 0039-6028/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.susc.2013.11.015
material of the 21st century for these applications can be found in a recent special issue [9]. One of the important challenges is the functionalization of graphene that involves interaction of graphene with atoms and molecules. Seiyama and coworkers (1962, [10]) explored the interaction of atoms and molecules with semiconductor surfaces that led them to produce the first chemo-resistive semiconductor gas sensors. However, oxides have proven themselves to be more reliable for the detection of different gases than semiconductors, and the most widely used material among oxides being SnO2 [11]. The variation of conductance of SnO2 thin films caused by surface reactions with the gas molecules is used as an indicator of the gas concentration. More recently, experimental and theoretical studies have shown that graphene can be used as a gas sensing material to detect various molecules, ranging from molecules in gas phase to some small bioactive molecules [12,13]. It is expected that graphene-based gas sensors should benefit from its exceptionally high mobility of charge carriers and structural stability. Graphene can be doped with carriers through interaction with donor and acceptor molecules [14]. Also, it is a promising material for applications that involve portable storage of gases, for example, bilayer graphene effectively stores hydrogen [15], as their interaction is neither too strong nor too weak. To fully explore the possibilities of graphene-based sensors or gasstorage systems, it is important to understand the interaction between graphene and the adsorbed molecules. The theoretical studies which focused on pristine graphene have predicted relatively low adsorption
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energies in comparison with the essential requirement of gas sensing applications [16,17]. However in reality the graphene sheets prepared by the available synthesis methods are likely to have many defects such as vacancies and substitutions [18]. Besides, the ability of graphene to sense or store gases can further be tuned with deliberate doping with non-carbon elements. Recently, the idea of doping graphene and assessing its interaction with H2S was theoretically explored by Zhang and coworkers [19]. These authors used Density Functional Theory (DFT) and nonequilibrium Green's-function formalism to inspect pristine, defective and doped graphene with transition metal atoms (like: Ca, Co and Fe). For doping with transition metal atoms, the affinity to bind with H2S was very high as compared to pristine graphene [19]. Moreover, if doped with Si, the adsorption was realized through the formation of Si\S bond [19]. In this context, our present work investigates the case of doping graphene with III–V semiconductors such as BN, which is a compromise between n-doping using N atoms, and the p-doping using B atoms. Furthermore, it is well known that substituting carbon hexagons with BN hexagons leads to the opening of gap [20] at Fermi level. The question that remains to be addressed here is the effect of this gap on the adsorption of H2S. Furthermore, the reduced dimensionality of graphene itself decreases the number of possible types of intrinsic defects [21]. Graphene lattice has the ability to reconstruct its structure by the formation of non-hexagonal rings. Among the experimentally observed intrinsic defects, the most common ones are Stone Wales, single vacancy, inverse Stone Wales and adatom defects. (i) Stone–Wales defect is formed when four hexagons are transformed into two pentagons and two heptagons (SW(55–77) defect) [22], by rotating one of the C\C bonds by 90°. The SW(55–77) defect has a formation energy of Ef ≈ 5 eV [23,24] with a barrier of approximately 9 eV. Once the defect is formed, the high barrier would warrant its thermodynamic stability. (ii) Single Vacancy is the simplest defect in any material, and correspond to a missing lattice atom. Atomic relaxation of this defect leads to the formation of a pentagon and a nine-membered ring (V1(5–9) defect). Ab-initio calculations yielded a formation energy of Ef ≈ 7.5 eV [25,26], which is much higher than that of SW defect and also higher than the formation energy of vacancies in many materials (e.g., 4.0 eV in Silicon [27]). (iii) Carbon Adatoms energetically favor the bridge configuration (i.e., on top of a carbon–carbon bond). Some degree of sp3-hybridization can appear locally so that two new covalent bonds can form between the adatom and the underlying atoms in the graphene plane. The binding energy of the carbon adatom is of the order of chemisorption 1.5– 2 eV [28,29]. (iv) Inverse Stone–Wales (ISW) defect is composed of two pentagons and two heptagons I2(7557), in which two pentagons are adjacent and separate two heptagons (this is an opposite configuration to SW defect). Ab-initio calculations estimate the formation energy to be Ef ≈ 5.8 eV [30], which is also higher than that of a SW defect, hence it is expected that the concentration of such a defect should be negligible. As far as its stability and its abundance are concerned [21], it would be interesting to study the effect of SW-defect on the adsorption of H2S molecule on graphene, this has not been studied before to the best of our knowledge. Native defects in materials usually play an important role in the modification of their mechanical, thermal and electronic properties. Among their positive effects in graphene, defects can lead to chemisorptions of some gases. Namely, Sanyal and coworkers [31] have reported that N2 molecule can dissolve in the vicinity of the carbon vacancy on graphene. Similar dissociation and adsorption by a vacancy in graphene were reported for other small gas molecules, such as H2 [32] and O2 [33]. Among the recent works on the adsorption of H2S on graphene with defects, Castellanos Aguila and coworkers [34] used DFT with the generalized-gradient approximation (GGA) in the parametrization of Perdew–Burke–Emzerhof to study pristine and defective graphene (including vacancy and substitution). They reported that H2S molecule can only be physisorbed on the surface of graphene. In this context, besides
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the doping of graphene with III–V group, our present work would pursue inspecting the interaction of H2S with graphene containing Stone– Wales (SW) defect. Especially, as the recent transmission-electron microscopy (TEM) has provided clear evidence about the abundance of SW defects in graphene [21]. Thus, one would be interested to see the effects of such defect with the inclusion of buckling [35] and relaxation on the interaction between SW-defect and H2S molecule. In the present work, we investigate the interaction and adsorption of the toxic H2S gas on graphene with and without defects or impurities using first-principles theoretical analysis. We organize the paper into four sections: with description of the computational methods in Section 2, results presented in Section 3 and conclusion in Section 4. 2. Computational methods In the present work, we use two computational methods. These two methods yield the same physical trends, and they complement one another. The first one is the self-consistent-charge density-functional tight-binding (SCC-DFTB) method [36,37], as implemented in the DFTB + package. We use Slater–Koster (SK) parameter files [38] from the ‘mio-0-1’ [39,40] set to parameterize the inter-atomic interactions. Van der Waals interaction was accounted for by using the LennardJones dispersion model as in DFTB + with parameters taken from the universal force field (UFF). Due to the unavailability of the SK parameter files for boron–sulfur interactions necessary for density functional tightbinding calculations, we used first-principles DFT as implemented in the Quantum ESPRESSO code [41] to study the adsorption of H2S molecule on the BN-doped graphene sheet. In these calculations, we use a plane wave basis set and ultrasoft pseudopotentials [42] to represent the interaction between ionic cores and valence electrons. Exchangecorrelation energy of electrons is treated within a local density approximation (LDA) of the Perdew–Zunger (PZ) parameterized form [43], which has been effectively used in previous works [19,34]. We use an energy cutoff of 30 Ry for the plane wave basis used for the wavefunctions, and 180 Ry for that used to represent charge density. We include the semi-empirical dispersion interactions (vdW) according to Barone et al. [44]. We note that the difference between energies calculated using DFTB and DFT is of the order of 10 meV per 50 atoms. Relaxed structures were determined through minimization of the total energy until Hellman–Feynman forces on each atom were smaller than 0.03 eV/Å in magnitude. The 2D sheet was simulated using a supercell geometry, with a vacuum layer of 20 Å separating adjacent periodic images of the sheet. Except when studying the dependence of adsorption capacity on the concentration of gas adsorbed on graphene, we used a supercell size of 5 × 5 × 1 unit cells (i.e., containing 50 carbon atoms). The Brillouin zone (BZ) was sampled using the Monkhorst–Pack technique [45], with a mesh of 24 × 24 × 1 in case of DFTB+, and a mesh of 6 × 6 × 1 in the case of Quantum ESPRESSO calculations. The binding energy of the gas molecule (i.e., the adsorption energy, Ebind) is calculated using the following convention: Ebind ¼ EðmoleculeþgrapheneÞ –EðgrapheneÞ –EðmoleculeÞ
ð1Þ
where E(molecule + graphene), E(graphene) and E(molecule) stand for the total energies of the relaxed molecule on graphene system, isolated graphene, and isolated molecule, respectively. The results of structural relaxations, electronic structure calculations and charge density plots are discussed in the next section. 3. Results and discussions 3.1. Structural relaxation with H2S molecule The relaxed structures of the three configurations of graphene: (a) pristine graphene (pG), (b) graphene with Stone–Wales defect;
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and (c) BN-doped graphene are shown in Fig. 1. In all these three systems, an H2S molecule was placed at a position close enough to bind to the graphene sheet. However, we observed that the molecule does not bind chemically to the sheet and rather moves away from it (as seen in the side-view in Fig. 1). The distances between the graphene sheet and the molecule, and the corresponding binding energies, depend weakly on the coverage (see Table 1). On the other hand, they do depend strongly on the site of adsorption (see Table 2). In the case of pristine graphene (pG), three different initial positions for H2S molecule were considered: (i) at the hollow site (H-pG); (ii) at the bond center (B-pG); and (iii) at the top of a C atomic site (S-pG). In all the three cases, the H2S molecule weakly binds to the pG sheet, and hence drifts away in a direction normal to the sheet, relaxing to a minimum energy at a distance of about 3.4 Å. The binding energies of adsorption at the sites (i), (ii) and (iii) are − 0.158 eV, − 0.153 eV, and − 0.153 eV, respectively, showing that the molecule at the hollow-site is energetically the most favorable configuration. We observe that the binding energies are almost entirely due to vdW interactions. Furthermore, the H2S molecule is shown to stabilize with sulfur atom closer to the graphene sheet, with the S\H bonds oriented upward. This orientation with a binding energy Eb ≈ −0.16 eV/molecule is consistent with the results of Zhang and coworkers [19] (whose Eb ≈ −0.13 eV/molecule). We have also assessed the effect of varying gas density (coverage) by changing the supercell size of pristine graphene (see Table 1). For all the supercell sizes, the molecule started from a hollow site near the surface, and eventually moved away in a direction perpendicular to the sheet and stabilized at a distance of about 3.4 Å with a binding energy of about −0.16 eV, independent of the system size. Hence, we infer that gas density would have a negligible effect on the adsorption of graphene. This is in contradiction with the reports of Castellanos Aguila et al. [34], who have shown that the interaction is weak and is of vdWtype but is dependent on the H2S coverage. Since they have considered
Table 1 The binding energy and the distance between H2S molecule and the pristine graphene sheet versus the system size (i.e., versus the gas density). Sample unit cells
Gas density molecule/Å2
3 4 5 6
21.2 11.9 7.64 5.30
× × × ×
3 4 5 6
× × × ×
10−3 10−3 10−3 10−3
DH2S–Surf Å
Ebind eV/molecule
3.48 3.44 3.47 3.37
−0.154 −0.158 −0.160 −0.161
higher concentrations of H2S, it is likely that their binding energy has contribution from H2S–H2S inter-interactions. Whereas, our binding energies do not show such a trend since we in the low-concentration regime (i.e., a single H2S molecule is used in relatively large supercells; the smallest one was 3 × 3 unit-cells). All the subsequent analysis was performed on a 5 × 5 supercell of graphene (with or without the inclusion of either a SW defect or doping with BN) and their interactions with a single H2S molecule were investigated. In the second case of graphene with SW-defect, two initial positions of H2S molecule were considered: (i) at the center of a defect pentagon, and (ii) at the center of a defect heptagon. In both these cases, the molecule stabilizes at the same local energy minimum, which is located at the hexagon interfacing with the pentagon of the defect (see Fig. 1). Hydrogen atoms of H2S are closer to the surface than its sulfur atom, which gives rise to a stronger vdW interaction between the molecule and the substrate, and the resulting attraction makes this configuration more favorable (see further details in the electronic structures and charge-density plots in Figs. 2 and 3, respectively). The distance of the molecule from the surface decreases to 2.86 Å and the binding energy increases to − 0.27 eV, much larger than the other sites considered here. This reveals that there exists a stronger attraction between the H2S molecule and the SW defects, and will be discussed in more details below. It is important to note that during relaxation, the graphene
Top View
Side View
(a) Pristine Graphene
(b) SW-Defected Graphene
(c) BN-Doped Graphene
Fig. 1. Relaxed atomic structures of H2S molecule on: (a) pristine graphene; (b) graphene with SW defect; (c) BN-doped graphene. The atomic species C, B, N, S and H are displayed in golden, light green, light blue, dark green and pink colors, respectively.
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Table 2 Comparison of the binding energy and the distance between H2S molecule and the graphene sheet in three cases: (a) pristine graphene; (b) SW-defected graphene; and (c) BN-doped graphene. The bond length of the molecule and angle are also given.
Pristine graphene Graphene with SW defect BN-doped graphene a b c
Ebin (eV/molecule) [k J/mole]
DH2S–Surf (Å)
DS–H (Å)
ΘHSH (degrees)
−0.16a [−15.4]a −0.12b[−11.8]b −0.13c −0.27a [−25.7]a−0.21b [−20.1]b −0.15b [−14.5]b −0.14c
3.47a 3.47c 2.86a 3.20b 3.22c
1.35a 1.35a 1.35b
97.12a 96.88a 92.02b
Results of DFTB. Results of Quantum Espresso. Reference [19].
sheet with SW defect warps due to the coupling of in-plane strain with G-band phonons (refer to Fig. 1b), as been reported by Shirodkar and Waghmare [35]. In the third case of BN-doped graphene, only one carbon ring was substituted by a BN-ring. The inclusion of BN hexagon(s) opens up an energy gap at Fermi level [20,46], and hence we investigate the effect of band gap opening on the interaction of H2S with HOMO eigenstate. We shall study this configuration using the Quantum ESPRESSO implementation of DFT since the SK-files describing the interactions between S and B atoms were unavailable for DFTB calculations. As in the adsorption at C-site, the molecule drifts away from the sheet and relaxes at a distance of 3.20 Å with a binding energy of −0.15 eV. The H2S molecule stabilizes in a configuration similar to that of adsorption at the C-site of pristine graphene, where the sulfur atom is closer to the surface than the hydrogen atoms. We conclude that the SW-defect site of graphene has a stronger interaction with the molecule than different sites of pristine or BN-doped graphene. We have further analyzed these interactions with charge density and electronic density of states (DOS) plots in Section 3.2.
3.2. Electronic band structures The total DOS (TDOS) and their projections on individual atoms (PDOS) as well as the band structures for the three systems, in configurations with inclusion of the H2S molecule are shown in Fig. 2. TDOS was normalized to the electronic content of a unit cell (i.e., 8 electrons/cell) with Fermi level taken as the reference. Fig. 2-a1 shows TDOS and PDOS's contributions in pristine graphene in presence of H2S molecule after relaxation. The vdW interaction does not have any effect of the electronic structure of graphene sheet. The vanishing gap with linear variation of PDOS of carbon atoms versus energy near Fermi level stems from the linear dispersion (Dirac cone at K-corner) of graphene, which is clearly shown in the band structure of Fig. 2-a2. Furthermore, Fig. 2-a1 clearly shows that the states of the molecule (sharp peaks associated with the 1s orbital of hydrogen and 3s and 3p orbitals of sulfur) are localized, and located away from Fermi level. One of these localized states, shown in dashed green line in Fig. 2-a2 (flat band at energy −2.37 eV), does correspond to the p-state orbital of sulfur. In comparison with the electronic DOS of pG (Fig. 2-a1), the TDOS of graphene with a SW defect (Fig. 2-b1) shows many peaks that correspond to the defect states as electronic states become more localized on the atoms at the SW defect (i.e., 2 pentagons + 2 heptagons). Fig. 2-b1 shows the TDOS and PDOS of the 5 × 5 supercell of the system of graphene with a SW defect and H2S molecule in the equilibrium configuration. Since the molecule is far from the surface, its electronic states do not hybridize with the surface states. From the perspective of band structure, Fig. 2-b2 clearly shows a small gap of 0.2 eV. This opening of gap is deceptive since the Dirac point shifts from the Г–K–M direction to another inequivalent high symmetry direction in the BZ for a 5 × 5 supercell (refer to reference [26]). In Fig. 2-b2, the H2S molecule introduces localized states as well (i.e., one flat band is clearly seen at − 2.37 eV, shown in green dashed line). This in turn confirms that the weak interaction between H2 S molecule and graphene sheet does not much affect the electronic structure of the sheet.
Fig. 2c shows the electronic DOS and bands of one BN-ring embedded in graphene matrix composed of 5 × 5 unit cells. Indeed, the BN-ring breaks the sublattice symmetry of graphene and perturbs the π-bonded electronic bands, which leads to the opening of a gap of about 0.3 eV (see TDOS and PDOS in Fig. 2-c1). This gap is not quite clear in the DOS as it is smeared out by the broadening/ smoothening and is clearer in the band structure shown in Fig. 2-c2. It is expected that the doping of graphene with more BN rings would enlarge the gap and make the material suitable for photonic applications [20]. It is evident (see Fig. 2-c1) that the molecular states remain sharp and do not interact with the surface states. One of the molecular orbitals, which originate from the p states of sulfur, is shown in Fig. 2c2 by the green-dashed line at same energy 2.37 eV below Fermi level. It is important to note that neither the Bloch-like extended states of BN-doped graphene nor those of pristine graphene do interact with the molecular states. 3.3. Charge-density distribution The contour plots of charge density projected on the plane of the sheet and the charge density plots of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states (i.e., The HOMO and LUMO states are the squared-amplitude of eigen-functions; they should be considered as representatives of hole and electron states, respectively.). These three quantities for the six systems (each of the three configurations with and without H2S molecule) are shown in Fig. 3. It is noted that there is no visible distinction between the contour plots with and without the H2S molecule since the interaction is of the weak vdW-type in all the cases. In Fig. 3a and b (pG without and with H2S), both HOMO and LUMO states are uniformly distributed over all carbon atoms. The H2S molecule has basically no effect on the planar charge density of graphene. More interestingly, the charge density of HOMO and LUMO states in the SW defect case (shown in Fig. 3c and d) gets localized to the defect sites. This leads to warping of the planar structure of graphene. The H2S molecule stabilizes closer to the interface of the SW pentagon and the neighboring hexagon. The hydrogen atoms are closer to the surface than the sulfur atom since they get attracted to the negative charges of the highest valence occupied states (HOMO and valence states which are a little lower in energy). Our calculations reveal that the change in the adsorption energy for pristine graphene and graphene with SW defect is entirely due to vdW interactions. Since the H atoms are closer to the surface of graphene with SW defect as compared to that of pristine graphene, the vdW interaction between the molecule and the SW defect is stronger. Hence the binding energy of H2S on graphene with SW defect is larger. Another possible explanation for the stronger vdW interaction between H2S molecule and graphene with SW-defect is that the HOMO state gets lowered in energy due to the molecule trying to seek a more stable configuration. Table 3 shows the energy of the HOMO level and total energy of the H2S molecule in three cases: (i) when it is free; (ii) when it is interacting with pristine graphene; and (iii) when it is interacting with graphene with SW defect. The energies are given in eV and the HOMO level of H2S molecule is not shifted by the Fermi energy as is the case in the DOS plots of Fig. 2. These results are obtained
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Fig. 2. Total and partial DOS and bands for: (a) pristine graphene; (b) SW-defected graphene; and (c) BN-doped graphene. These three systems are studied with H2S molecule. TDOS is normalized to one primitive cell and Fermi level is taken as an energy reference. In all the three shown band structures, the molecular level of H2S (due to p-orbitals of sulfur) is shown by the green-dashed line at energy −2.37 eV.
by using the DFTB code. They clearly show that when the distance between the molecule and the surface decreases both the HOMO level in H2S molecule and its total energy decrease, indicating that the molecule achieves more stability.
In the third case of BN-doped graphene (shown in Fig. 3e), nitrogen is more electronegative than carbon, and hence attracts more charge towards itself (see HOMO state in Fig. 3e). Hence, the BN-ring breaks the sublattice symmetry of graphene and perturbs the π-bonding.
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Contour Plot
HOMO
173
LUMO
(a) pG
(b) pG with H2S
(c) SW defect
(d) SW defect & H2S
(e) BN-pG
(f) BN-pG & H2S
Fig. 3. Contour plots of the total charge density and charge density plots of the HOMO and LUMO states for the systems of Fig. 2 (with and without H2S molecule). The charges localized on HOMO and LUMO are displayed in navy-blue color. The atomic species C, B, N, S and H are displayed in golden, silver, sky-blue, green and pink colors, respectively.
Nonetheless, the HOMO is still uniformly distributed as a Bloch-like extended state (see charges on every other site starting from nitrogen in Fig. 3e). The LUMO is also uniformly distributed, but on the sites alternating those hosting the HOMO states. In the presence of the H2S molecule, the charge distribution on the plane remains almost the same as that without the molecule (see Fig. 3f). This uniformity of HOMO and LUMO states would not lead to any significant enhancement of adsorption of the H2S molecule on the surface, and is of the same order as that of pristine graphene (shown in Fig. 3b).
Table 3 The results of HOMO energy and total energy of H2S molecule, obtained by DFTB code, are shown for a contrast between three cases: (i) free H2S molecule, (ii) H2S molecule interacting with pristine graphene, and (iii) H2S molecule interacting with graphene with SW defect. EHOMO is not shifted by Fermi energy.
EHOMO (H2S) “eV” ETOT (H2S) “eV”
Free H2S molecule
H2S on pristine graphene
H2S on graphene with SW defect
−6.685 −85.438
−6.709 −85.520
−6.730 −85.580
4. Conclusions Both DFTB and DFT based calculations have been carried out to investigate the nature of interaction of the toxic H2S gas molecule with graphene. The investigation has focused on the interaction of the H2S molecule with three systems with chemically different sites: (i) pristine graphene; (ii) graphene with a Stone–Wales defect; and (iii) BN-doped graphene. We have studied the electronic structure and charge density distribution for these three systems. The calculations took into account the vdW interactions, and our results show the following trends: (i) In the cases of pristine graphene and BN-doped graphene, the charge density of HOMO and LUMO states is uniformly distributed throughout the graphene sublattice and consequently they do not have a significant effect on the adsorption of the gas. The H2S molecule hence relaxes at a far-off distance of ~ 3.5 Å from the surface. The molecule is bound to the sheet via van der Waals interaction with a weak binding energy of about − 0.16 eV/molecule. (ii) In the case of graphene with Stone–Wales defect, the HOMO and LUMO states are confined to the alternating sites of the SW defect. Since the molecule is closer to the surface of graphene with SW defect (~ 2.86 Å with H atoms of H2S being closer to
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graphene), the van der Waals interaction between the molecule and the surface is stronger. Hence, the resulting binding energy is larger as compared to that of pristine and BN-doped graphene. Another signature of stability is that the HOMO level in the H2S molecule and its total energy get further lowered as compared to those of pG and BN-doped graphene. (iii) All the studied cases remain to be within the domain of physisorption. Thus, pristine, graphene with defects and that doped with III–V semiconductors should be relevant for storage of H2S but not for gas sensing. Our work shows how point topological defects in graphene are effective in capturing a gas like H2S. Since the adsorption energy (26 k J/mol) is considerably larger than the thermal energy at room temperature (2.5 k J/mol), the gas will not be easily desorbed from the surface of graphene with Stone–Wales defect. This property should be further explored in enhancing the storage of H 2S gas on graphene with defects. Acknowledgments The authors are indebted to thank A. Mishra, A. Sunaidi and N. Tabet for many fruitful discussions. S.N.S. is grateful to the council of scientific and industrial research, India, for a research fellowship. One of us (N.T.) benefited from a visit to KFUPM in summer 2011, when this work was started, and from another visit to JNCASR in summer 2012, where this work was completed.
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First principles analysis of graphene and its ability to maintain long-ranged interaction with H2S Vinay I. Hegde a, Sharmila N. Shirodkar a, Nacir Tit b,⁎, Umesh V. Waghmare a, Zain H. Yamani c a b c
Theoretical Sciences Unit and Sheikh Saqr Laboratory, Jawaharlal Nehru Center for Advanced Scientific Research, Bangalore 560 064, India Physics Department, UAE University, P.O. Box 17551, Al-Ain, United Arab Emirates Center for Research Excellence in Nanotechnology, King Fahd University of Petroleum and Minerals, P.O. Box 5040, 31261 Dhahran, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 3 June 2013 Accepted 23 November 2013 Available online 1 December 2013 Keywords: Electronic structure of graphene Impurity and defect levels Adsorption kinetics Desorption kinetics
a b s t r a c t We determine the chemical activity of (a) carbon site of pristine graphene, (b) Stone–Wales (SW) defect site, and (c) BN-sites of BN-doped graphene towards adsorption of a toxic gas H2S, through comparative analysis based on first-principles density functional theoretical calculations incorporating van der Waals (vdW) interactions. While the adsorption of H2S is weak at both C and BN sites with a binding energy of 15 k J/mol, it is significantly stronger at the Stone–Wales defect site with a much higher binding energy of 26 k J/mol. This is clearly reflected in the contrasting orientation of H2S molecule in the relaxed geometries: the sulfur atom of H2S is closer to graphene (at a distance 3.14 Å) during physisorption at C and BN sites, while the molecule's H atoms come closer to graphene (at a distance 2.84 Å) during physisorption at the Stone–Wales defect site. The origin of the stronger binding interaction between H2S and a SW defect site is attributed to two possible reasons: (i) an increase in the vdW interaction; and (ii) the lowering of both energy of the HOMO level and the total energy of the H2S molecule in attaining a stable configuration. Our findings are compared to the available theoretical results and their technological relevance is further discussed. © 2013 Published by Elsevier B.V.
1. Introduction The pioneering research work of Geim and Novoselov [1] on graphene has opened up a new horizon for fundamental research, and a wide range of advanced technological applications [2]. Graphene possesses unique combination of mechanical strength and flexibility, structural and electronic properties, which makes it attractive for materials engineering. The electronic structure of graphene exhibits linear dispersion near the Fermi level (i.e., Dirac cones at K-points of the Brillouin zone). As a result, effective dynamics of electrons in graphene is that of a massless Dirac (relativistic) fermion, and graphene's electron mobility is rather high (~ 105 cm2 V−1 s−1) [1]. These properties are advantageous in the development of high-speed next generation devices with characteristics exceeding those of silicon and conventional semiconductors. Applications of graphene are quite diverse and relate to interesting physical mechanisms: (1) nanoelectronics (e.g., synthesis of the smallest transistor [3]); (2) photonics (e.g., band-gap engineering using quantum confinement effects in nano-ribbons [4], and BN doping [5]); (3) spintronics (e.g., induction of ferromagnetism by the adsorbed hydrogen atoms in nanoribbons [6]); and (4) gas sensing (e.g., ability to detect several gases like CO, CO2, NO, NO2 and NH3 [7,8]). A very nice coverage of physical challenges involved in making graphene as the ⁎ Corresponding author. E-mail address: [email protected] (N. Tit). 0039-6028/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.susc.2013.11.015
material of the 21st century for these applications can be found in a recent special issue [9]. One of the important challenges is the functionalization of graphene that involves interaction of graphene with atoms and molecules. Seiyama and coworkers (1962, [10]) explored the interaction of atoms and molecules with semiconductor surfaces that led them to produce the first chemo-resistive semiconductor gas sensors. However, oxides have proven themselves to be more reliable for the detection of different gases than semiconductors, and the most widely used material among oxides being SnO2 [11]. The variation of conductance of SnO2 thin films caused by surface reactions with the gas molecules is used as an indicator of the gas concentration. More recently, experimental and theoretical studies have shown that graphene can be used as a gas sensing material to detect various molecules, ranging from molecules in gas phase to some small bioactive molecules [12,13]. It is expected that graphene-based gas sensors should benefit from its exceptionally high mobility of charge carriers and structural stability. Graphene can be doped with carriers through interaction with donor and acceptor molecules [14]. Also, it is a promising material for applications that involve portable storage of gases, for example, bilayer graphene effectively stores hydrogen [15], as their interaction is neither too strong nor too weak. To fully explore the possibilities of graphene-based sensors or gasstorage systems, it is important to understand the interaction between graphene and the adsorbed molecules. The theoretical studies which focused on pristine graphene have predicted relatively low adsorption
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energies in comparison with the essential requirement of gas sensing applications [16,17]. However in reality the graphene sheets prepared by the available synthesis methods are likely to have many defects such as vacancies and substitutions [18]. Besides, the ability of graphene to sense or store gases can further be tuned with deliberate doping with non-carbon elements. Recently, the idea of doping graphene and assessing its interaction with H2S was theoretically explored by Zhang and coworkers [19]. These authors used Density Functional Theory (DFT) and nonequilibrium Green's-function formalism to inspect pristine, defective and doped graphene with transition metal atoms (like: Ca, Co and Fe). For doping with transition metal atoms, the affinity to bind with H2S was very high as compared to pristine graphene [19]. Moreover, if doped with Si, the adsorption was realized through the formation of Si\S bond [19]. In this context, our present work investigates the case of doping graphene with III–V semiconductors such as BN, which is a compromise between n-doping using N atoms, and the p-doping using B atoms. Furthermore, it is well known that substituting carbon hexagons with BN hexagons leads to the opening of gap [20] at Fermi level. The question that remains to be addressed here is the effect of this gap on the adsorption of H2S. Furthermore, the reduced dimensionality of graphene itself decreases the number of possible types of intrinsic defects [21]. Graphene lattice has the ability to reconstruct its structure by the formation of non-hexagonal rings. Among the experimentally observed intrinsic defects, the most common ones are Stone Wales, single vacancy, inverse Stone Wales and adatom defects. (i) Stone–Wales defect is formed when four hexagons are transformed into two pentagons and two heptagons (SW(55–77) defect) [22], by rotating one of the C\C bonds by 90°. The SW(55–77) defect has a formation energy of Ef ≈ 5 eV [23,24] with a barrier of approximately 9 eV. Once the defect is formed, the high barrier would warrant its thermodynamic stability. (ii) Single Vacancy is the simplest defect in any material, and correspond to a missing lattice atom. Atomic relaxation of this defect leads to the formation of a pentagon and a nine-membered ring (V1(5–9) defect). Ab-initio calculations yielded a formation energy of Ef ≈ 7.5 eV [25,26], which is much higher than that of SW defect and also higher than the formation energy of vacancies in many materials (e.g., 4.0 eV in Silicon [27]). (iii) Carbon Adatoms energetically favor the bridge configuration (i.e., on top of a carbon–carbon bond). Some degree of sp3-hybridization can appear locally so that two new covalent bonds can form between the adatom and the underlying atoms in the graphene plane. The binding energy of the carbon adatom is of the order of chemisorption 1.5– 2 eV [28,29]. (iv) Inverse Stone–Wales (ISW) defect is composed of two pentagons and two heptagons I2(7557), in which two pentagons are adjacent and separate two heptagons (this is an opposite configuration to SW defect). Ab-initio calculations estimate the formation energy to be Ef ≈ 5.8 eV [30], which is also higher than that of a SW defect, hence it is expected that the concentration of such a defect should be negligible. As far as its stability and its abundance are concerned [21], it would be interesting to study the effect of SW-defect on the adsorption of H2S molecule on graphene, this has not been studied before to the best of our knowledge. Native defects in materials usually play an important role in the modification of their mechanical, thermal and electronic properties. Among their positive effects in graphene, defects can lead to chemisorptions of some gases. Namely, Sanyal and coworkers [31] have reported that N2 molecule can dissolve in the vicinity of the carbon vacancy on graphene. Similar dissociation and adsorption by a vacancy in graphene were reported for other small gas molecules, such as H2 [32] and O2 [33]. Among the recent works on the adsorption of H2S on graphene with defects, Castellanos Aguila and coworkers [34] used DFT with the generalized-gradient approximation (GGA) in the parametrization of Perdew–Burke–Emzerhof to study pristine and defective graphene (including vacancy and substitution). They reported that H2S molecule can only be physisorbed on the surface of graphene. In this context, besides
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the doping of graphene with III–V group, our present work would pursue inspecting the interaction of H2S with graphene containing Stone– Wales (SW) defect. Especially, as the recent transmission-electron microscopy (TEM) has provided clear evidence about the abundance of SW defects in graphene [21]. Thus, one would be interested to see the effects of such defect with the inclusion of buckling [35] and relaxation on the interaction between SW-defect and H2S molecule. In the present work, we investigate the interaction and adsorption of the toxic H2S gas on graphene with and without defects or impurities using first-principles theoretical analysis. We organize the paper into four sections: with description of the computational methods in Section 2, results presented in Section 3 and conclusion in Section 4. 2. Computational methods In the present work, we use two computational methods. These two methods yield the same physical trends, and they complement one another. The first one is the self-consistent-charge density-functional tight-binding (SCC-DFTB) method [36,37], as implemented in the DFTB + package. We use Slater–Koster (SK) parameter files [38] from the ‘mio-0-1’ [39,40] set to parameterize the inter-atomic interactions. Van der Waals interaction was accounted for by using the LennardJones dispersion model as in DFTB + with parameters taken from the universal force field (UFF). Due to the unavailability of the SK parameter files for boron–sulfur interactions necessary for density functional tightbinding calculations, we used first-principles DFT as implemented in the Quantum ESPRESSO code [41] to study the adsorption of H2S molecule on the BN-doped graphene sheet. In these calculations, we use a plane wave basis set and ultrasoft pseudopotentials [42] to represent the interaction between ionic cores and valence electrons. Exchangecorrelation energy of electrons is treated within a local density approximation (LDA) of the Perdew–Zunger (PZ) parameterized form [43], which has been effectively used in previous works [19,34]. We use an energy cutoff of 30 Ry for the plane wave basis used for the wavefunctions, and 180 Ry for that used to represent charge density. We include the semi-empirical dispersion interactions (vdW) according to Barone et al. [44]. We note that the difference between energies calculated using DFTB and DFT is of the order of 10 meV per 50 atoms. Relaxed structures were determined through minimization of the total energy until Hellman–Feynman forces on each atom were smaller than 0.03 eV/Å in magnitude. The 2D sheet was simulated using a supercell geometry, with a vacuum layer of 20 Å separating adjacent periodic images of the sheet. Except when studying the dependence of adsorption capacity on the concentration of gas adsorbed on graphene, we used a supercell size of 5 × 5 × 1 unit cells (i.e., containing 50 carbon atoms). The Brillouin zone (BZ) was sampled using the Monkhorst–Pack technique [45], with a mesh of 24 × 24 × 1 in case of DFTB+, and a mesh of 6 × 6 × 1 in the case of Quantum ESPRESSO calculations. The binding energy of the gas molecule (i.e., the adsorption energy, Ebind) is calculated using the following convention: Ebind ¼ EðmoleculeþgrapheneÞ –EðgrapheneÞ –EðmoleculeÞ
ð1Þ
where E(molecule + graphene), E(graphene) and E(molecule) stand for the total energies of the relaxed molecule on graphene system, isolated graphene, and isolated molecule, respectively. The results of structural relaxations, electronic structure calculations and charge density plots are discussed in the next section. 3. Results and discussions 3.1. Structural relaxation with H2S molecule The relaxed structures of the three configurations of graphene: (a) pristine graphene (pG), (b) graphene with Stone–Wales defect;
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and (c) BN-doped graphene are shown in Fig. 1. In all these three systems, an H2S molecule was placed at a position close enough to bind to the graphene sheet. However, we observed that the molecule does not bind chemically to the sheet and rather moves away from it (as seen in the side-view in Fig. 1). The distances between the graphene sheet and the molecule, and the corresponding binding energies, depend weakly on the coverage (see Table 1). On the other hand, they do depend strongly on the site of adsorption (see Table 2). In the case of pristine graphene (pG), three different initial positions for H2S molecule were considered: (i) at the hollow site (H-pG); (ii) at the bond center (B-pG); and (iii) at the top of a C atomic site (S-pG). In all the three cases, the H2S molecule weakly binds to the pG sheet, and hence drifts away in a direction normal to the sheet, relaxing to a minimum energy at a distance of about 3.4 Å. The binding energies of adsorption at the sites (i), (ii) and (iii) are − 0.158 eV, − 0.153 eV, and − 0.153 eV, respectively, showing that the molecule at the hollow-site is energetically the most favorable configuration. We observe that the binding energies are almost entirely due to vdW interactions. Furthermore, the H2S molecule is shown to stabilize with sulfur atom closer to the graphene sheet, with the S\H bonds oriented upward. This orientation with a binding energy Eb ≈ −0.16 eV/molecule is consistent with the results of Zhang and coworkers [19] (whose Eb ≈ −0.13 eV/molecule). We have also assessed the effect of varying gas density (coverage) by changing the supercell size of pristine graphene (see Table 1). For all the supercell sizes, the molecule started from a hollow site near the surface, and eventually moved away in a direction perpendicular to the sheet and stabilized at a distance of about 3.4 Å with a binding energy of about −0.16 eV, independent of the system size. Hence, we infer that gas density would have a negligible effect on the adsorption of graphene. This is in contradiction with the reports of Castellanos Aguila et al. [34], who have shown that the interaction is weak and is of vdWtype but is dependent on the H2S coverage. Since they have considered
Table 1 The binding energy and the distance between H2S molecule and the pristine graphene sheet versus the system size (i.e., versus the gas density). Sample unit cells
Gas density molecule/Å2
3 4 5 6
21.2 11.9 7.64 5.30
× × × ×
3 4 5 6
× × × ×
10−3 10−3 10−3 10−3
DH2S–Surf Å
Ebind eV/molecule
3.48 3.44 3.47 3.37
−0.154 −0.158 −0.160 −0.161
higher concentrations of H2S, it is likely that their binding energy has contribution from H2S–H2S inter-interactions. Whereas, our binding energies do not show such a trend since we in the low-concentration regime (i.e., a single H2S molecule is used in relatively large supercells; the smallest one was 3 × 3 unit-cells). All the subsequent analysis was performed on a 5 × 5 supercell of graphene (with or without the inclusion of either a SW defect or doping with BN) and their interactions with a single H2S molecule were investigated. In the second case of graphene with SW-defect, two initial positions of H2S molecule were considered: (i) at the center of a defect pentagon, and (ii) at the center of a defect heptagon. In both these cases, the molecule stabilizes at the same local energy minimum, which is located at the hexagon interfacing with the pentagon of the defect (see Fig. 1). Hydrogen atoms of H2S are closer to the surface than its sulfur atom, which gives rise to a stronger vdW interaction between the molecule and the substrate, and the resulting attraction makes this configuration more favorable (see further details in the electronic structures and charge-density plots in Figs. 2 and 3, respectively). The distance of the molecule from the surface decreases to 2.86 Å and the binding energy increases to − 0.27 eV, much larger than the other sites considered here. This reveals that there exists a stronger attraction between the H2S molecule and the SW defects, and will be discussed in more details below. It is important to note that during relaxation, the graphene
Top View
Side View
(a) Pristine Graphene
(b) SW-Defected Graphene
(c) BN-Doped Graphene
Fig. 1. Relaxed atomic structures of H2S molecule on: (a) pristine graphene; (b) graphene with SW defect; (c) BN-doped graphene. The atomic species C, B, N, S and H are displayed in golden, light green, light blue, dark green and pink colors, respectively.
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Table 2 Comparison of the binding energy and the distance between H2S molecule and the graphene sheet in three cases: (a) pristine graphene; (b) SW-defected graphene; and (c) BN-doped graphene. The bond length of the molecule and angle are also given.
Pristine graphene Graphene with SW defect BN-doped graphene a b c
Ebin (eV/molecule) [k J/mole]
DH2S–Surf (Å)
DS–H (Å)
ΘHSH (degrees)
−0.16a [−15.4]a −0.12b[−11.8]b −0.13c −0.27a [−25.7]a−0.21b [−20.1]b −0.15b [−14.5]b −0.14c
3.47a 3.47c 2.86a 3.20b 3.22c
1.35a 1.35a 1.35b
97.12a 96.88a 92.02b
Results of DFTB. Results of Quantum Espresso. Reference [19].
sheet with SW defect warps due to the coupling of in-plane strain with G-band phonons (refer to Fig. 1b), as been reported by Shirodkar and Waghmare [35]. In the third case of BN-doped graphene, only one carbon ring was substituted by a BN-ring. The inclusion of BN hexagon(s) opens up an energy gap at Fermi level [20,46], and hence we investigate the effect of band gap opening on the interaction of H2S with HOMO eigenstate. We shall study this configuration using the Quantum ESPRESSO implementation of DFT since the SK-files describing the interactions between S and B atoms were unavailable for DFTB calculations. As in the adsorption at C-site, the molecule drifts away from the sheet and relaxes at a distance of 3.20 Å with a binding energy of −0.15 eV. The H2S molecule stabilizes in a configuration similar to that of adsorption at the C-site of pristine graphene, where the sulfur atom is closer to the surface than the hydrogen atoms. We conclude that the SW-defect site of graphene has a stronger interaction with the molecule than different sites of pristine or BN-doped graphene. We have further analyzed these interactions with charge density and electronic density of states (DOS) plots in Section 3.2.
3.2. Electronic band structures The total DOS (TDOS) and their projections on individual atoms (PDOS) as well as the band structures for the three systems, in configurations with inclusion of the H2S molecule are shown in Fig. 2. TDOS was normalized to the electronic content of a unit cell (i.e., 8 electrons/cell) with Fermi level taken as the reference. Fig. 2-a1 shows TDOS and PDOS's contributions in pristine graphene in presence of H2S molecule after relaxation. The vdW interaction does not have any effect of the electronic structure of graphene sheet. The vanishing gap with linear variation of PDOS of carbon atoms versus energy near Fermi level stems from the linear dispersion (Dirac cone at K-corner) of graphene, which is clearly shown in the band structure of Fig. 2-a2. Furthermore, Fig. 2-a1 clearly shows that the states of the molecule (sharp peaks associated with the 1s orbital of hydrogen and 3s and 3p orbitals of sulfur) are localized, and located away from Fermi level. One of these localized states, shown in dashed green line in Fig. 2-a2 (flat band at energy −2.37 eV), does correspond to the p-state orbital of sulfur. In comparison with the electronic DOS of pG (Fig. 2-a1), the TDOS of graphene with a SW defect (Fig. 2-b1) shows many peaks that correspond to the defect states as electronic states become more localized on the atoms at the SW defect (i.e., 2 pentagons + 2 heptagons). Fig. 2-b1 shows the TDOS and PDOS of the 5 × 5 supercell of the system of graphene with a SW defect and H2S molecule in the equilibrium configuration. Since the molecule is far from the surface, its electronic states do not hybridize with the surface states. From the perspective of band structure, Fig. 2-b2 clearly shows a small gap of 0.2 eV. This opening of gap is deceptive since the Dirac point shifts from the Г–K–M direction to another inequivalent high symmetry direction in the BZ for a 5 × 5 supercell (refer to reference [26]). In Fig. 2-b2, the H2S molecule introduces localized states as well (i.e., one flat band is clearly seen at − 2.37 eV, shown in green dashed line). This in turn confirms that the weak interaction between H2 S molecule and graphene sheet does not much affect the electronic structure of the sheet.
Fig. 2c shows the electronic DOS and bands of one BN-ring embedded in graphene matrix composed of 5 × 5 unit cells. Indeed, the BN-ring breaks the sublattice symmetry of graphene and perturbs the π-bonded electronic bands, which leads to the opening of a gap of about 0.3 eV (see TDOS and PDOS in Fig. 2-c1). This gap is not quite clear in the DOS as it is smeared out by the broadening/ smoothening and is clearer in the band structure shown in Fig. 2-c2. It is expected that the doping of graphene with more BN rings would enlarge the gap and make the material suitable for photonic applications [20]. It is evident (see Fig. 2-c1) that the molecular states remain sharp and do not interact with the surface states. One of the molecular orbitals, which originate from the p states of sulfur, is shown in Fig. 2c2 by the green-dashed line at same energy 2.37 eV below Fermi level. It is important to note that neither the Bloch-like extended states of BN-doped graphene nor those of pristine graphene do interact with the molecular states. 3.3. Charge-density distribution The contour plots of charge density projected on the plane of the sheet and the charge density plots of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states (i.e., The HOMO and LUMO states are the squared-amplitude of eigen-functions; they should be considered as representatives of hole and electron states, respectively.). These three quantities for the six systems (each of the three configurations with and without H2S molecule) are shown in Fig. 3. It is noted that there is no visible distinction between the contour plots with and without the H2S molecule since the interaction is of the weak vdW-type in all the cases. In Fig. 3a and b (pG without and with H2S), both HOMO and LUMO states are uniformly distributed over all carbon atoms. The H2S molecule has basically no effect on the planar charge density of graphene. More interestingly, the charge density of HOMO and LUMO states in the SW defect case (shown in Fig. 3c and d) gets localized to the defect sites. This leads to warping of the planar structure of graphene. The H2S molecule stabilizes closer to the interface of the SW pentagon and the neighboring hexagon. The hydrogen atoms are closer to the surface than the sulfur atom since they get attracted to the negative charges of the highest valence occupied states (HOMO and valence states which are a little lower in energy). Our calculations reveal that the change in the adsorption energy for pristine graphene and graphene with SW defect is entirely due to vdW interactions. Since the H atoms are closer to the surface of graphene with SW defect as compared to that of pristine graphene, the vdW interaction between the molecule and the SW defect is stronger. Hence the binding energy of H2S on graphene with SW defect is larger. Another possible explanation for the stronger vdW interaction between H2S molecule and graphene with SW-defect is that the HOMO state gets lowered in energy due to the molecule trying to seek a more stable configuration. Table 3 shows the energy of the HOMO level and total energy of the H2S molecule in three cases: (i) when it is free; (ii) when it is interacting with pristine graphene; and (iii) when it is interacting with graphene with SW defect. The energies are given in eV and the HOMO level of H2S molecule is not shifted by the Fermi energy as is the case in the DOS plots of Fig. 2. These results are obtained
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Fig. 2. Total and partial DOS and bands for: (a) pristine graphene; (b) SW-defected graphene; and (c) BN-doped graphene. These three systems are studied with H2S molecule. TDOS is normalized to one primitive cell and Fermi level is taken as an energy reference. In all the three shown band structures, the molecular level of H2S (due to p-orbitals of sulfur) is shown by the green-dashed line at energy −2.37 eV.
by using the DFTB code. They clearly show that when the distance between the molecule and the surface decreases both the HOMO level in H2S molecule and its total energy decrease, indicating that the molecule achieves more stability.
In the third case of BN-doped graphene (shown in Fig. 3e), nitrogen is more electronegative than carbon, and hence attracts more charge towards itself (see HOMO state in Fig. 3e). Hence, the BN-ring breaks the sublattice symmetry of graphene and perturbs the π-bonding.
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Contour Plot
HOMO
173
LUMO
(a) pG
(b) pG with H2S
(c) SW defect
(d) SW defect & H2S
(e) BN-pG
(f) BN-pG & H2S
Fig. 3. Contour plots of the total charge density and charge density plots of the HOMO and LUMO states for the systems of Fig. 2 (with and without H2S molecule). The charges localized on HOMO and LUMO are displayed in navy-blue color. The atomic species C, B, N, S and H are displayed in golden, silver, sky-blue, green and pink colors, respectively.
Nonetheless, the HOMO is still uniformly distributed as a Bloch-like extended state (see charges on every other site starting from nitrogen in Fig. 3e). The LUMO is also uniformly distributed, but on the sites alternating those hosting the HOMO states. In the presence of the H2S molecule, the charge distribution on the plane remains almost the same as that without the molecule (see Fig. 3f). This uniformity of HOMO and LUMO states would not lead to any significant enhancement of adsorption of the H2S molecule on the surface, and is of the same order as that of pristine graphene (shown in Fig. 3b).
Table 3 The results of HOMO energy and total energy of H2S molecule, obtained by DFTB code, are shown for a contrast between three cases: (i) free H2S molecule, (ii) H2S molecule interacting with pristine graphene, and (iii) H2S molecule interacting with graphene with SW defect. EHOMO is not shifted by Fermi energy.
EHOMO (H2S) “eV” ETOT (H2S) “eV”
Free H2S molecule
H2S on pristine graphene
H2S on graphene with SW defect
−6.685 −85.438
−6.709 −85.520
−6.730 −85.580
4. Conclusions Both DFTB and DFT based calculations have been carried out to investigate the nature of interaction of the toxic H2S gas molecule with graphene. The investigation has focused on the interaction of the H2S molecule with three systems with chemically different sites: (i) pristine graphene; (ii) graphene with a Stone–Wales defect; and (iii) BN-doped graphene. We have studied the electronic structure and charge density distribution for these three systems. The calculations took into account the vdW interactions, and our results show the following trends: (i) In the cases of pristine graphene and BN-doped graphene, the charge density of HOMO and LUMO states is uniformly distributed throughout the graphene sublattice and consequently they do not have a significant effect on the adsorption of the gas. The H2S molecule hence relaxes at a far-off distance of ~ 3.5 Å from the surface. The molecule is bound to the sheet via van der Waals interaction with a weak binding energy of about − 0.16 eV/molecule. (ii) In the case of graphene with Stone–Wales defect, the HOMO and LUMO states are confined to the alternating sites of the SW defect. Since the molecule is closer to the surface of graphene with SW defect (~ 2.86 Å with H atoms of H2S being closer to
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graphene), the van der Waals interaction between the molecule and the surface is stronger. Hence, the resulting binding energy is larger as compared to that of pristine and BN-doped graphene. Another signature of stability is that the HOMO level in the H2S molecule and its total energy get further lowered as compared to those of pG and BN-doped graphene. (iii) All the studied cases remain to be within the domain of physisorption. Thus, pristine, graphene with defects and that doped with III–V semiconductors should be relevant for storage of H2S but not for gas sensing. Our work shows how point topological defects in graphene are effective in capturing a gas like H2S. Since the adsorption energy (26 k J/mol) is considerably larger than the thermal energy at room temperature (2.5 k J/mol), the gas will not be easily desorbed from the surface of graphene with Stone–Wales defect. This property should be further explored in enhancing the storage of H 2S gas on graphene with defects. Acknowledgments The authors are indebted to thank A. Mishra, A. Sunaidi and N. Tabet for many fruitful discussions. S.N.S. is grateful to the council of scientific and industrial research, India, for a research fellowship. One of us (N.T.) benefited from a visit to KFUPM in summer 2011, when this work was started, and from another visit to JNCASR in summer 2012, where this work was completed.
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